value of the discriminant and give the number of solutions to the quadratic equation?

Question

-5 x ^2 - x - 4 = 0

Discriminant=
Number of Real Solutions=

Answer 1

discriminant = (-1)^2 - 4(-4)(-5) = 1 - 80 = -79
# of real solutions = 0

general case:
ax^2 + bx + c = 0

discriminant = b^2 - 4ac
number of real solutions = 0 if disc < 0, 1 if disc = 0, 2 if disc > 0

Answer 2

Multiply both sides by -1 getting,
5x^2 + x + 4 = 0; now divide both sides by 5 to get
x^2 + x/5 + 4/5 = 0. NOw use the quadratic equation to get x:

x = (-1/5 +- SQR[(1/5)(1/5) - 4(1)(4/5)])/2(1)

where the +- refers to each equation. And the value of SQR[above] = i*SQR(79)/5 such that there are two complex solutions:

x=-1/5 +- i*SQR(79)/5